A363897 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k)).

1, 2, 3, 4, 5, 7, 7, 8, 9, 10, 12, 14, 13, 14, 15, 17, 17, 21, 19, 20, 22, 24, 23, 28, 25, 27, 27, 28, 29, 35, 32, 34, 36, 34, 35, 43, 37, 38, 39, 40, 42, 51, 43, 48, 45, 47, 47, 59, 49, 50, 52, 54, 53, 63, 60, 57, 57, 58, 59, 70, 62, 64, 66, 68, 65, 84, 67, 68, 69, 70, 72, 86, 73, 74, 75, 77, 84, 94

Offset: 1

Author

Seiichi Manyama, Jun 27 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A363898, A363899, A363900.

Cf. A002131, A050460, A326399.

Cf. A001876, A284097.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d%5==1)*d);

Formula

a(n) = Sum_{d|n, n/d==1 mod 5} d.

G.f.: Sum_{k>0} x^(5*k-4) / (1 - x^(5*k-4))^2.